In-depth development and assessment of covariance models for multivariate nonstationary processes on a sphere

随着科学技术的进步，许多地球物理问题涉及全球范围内的数据集，具有多个感兴趣的变量。因此，有一个迫切需要灵活的非平稳协方差模型的多变量过程定义在一个球体上。另一方面，在开发地质统计数据协方差模型的同时，还应制定对拟议模型进行全面拟合优度诊断的方法。该项目的目标是提供多变量空间（时间）协方差模型在一个球域上的深入发展，解决协方差结构的某些非平稳特性，在小规模和大规模，与建议的模型的全面拟合优度诊断配对。建议的协方差模型是灵活的捕捉复杂的非平稳性，如变化的平滑度和几何各向异性。研究人员开发贝叶斯和非贝叶斯方法的拟合优度诊断，并研究插件的协方差模型估计的影响。研究人员将该项目中开发的模型应用于验证CMIP 5档案中多个气候模型输出的问题，并对模型拟合进行彻底诊断。不同的协方差结构在陆地和海洋，以及它们对纬度的依赖性，进行了深入的研究。研究人员还探索了大型数据集的有效计算方法。该项目的动机是结合多个气候模式输出和研究不同气候变量之间关系的科学问题。世界各地的气候科学家正在投入大量努力开发最先进的气候模型，一套新的气候模型输出（CMIP 5-耦合模型相互比较项目第5阶段）正在出现，这是政府间气候变化专门委员会（气专委）第五次评估报告结果的基础。该项目将为气候科学家和气候建模者提供有用的工具，以相互比较和联合收割机气候模型，并测试CMIP 5结果相对于先前CMIP 3结果的改进。该项目开发的统计模型将能够更准确地评估温度和降水等多个气候变量与未来气候变化之间的关系。

With the advancement of science and technology, many geophysical problems involve data sets on a global scale with multiple variables of interest. As a consequence, there is a pressing need for flexible nonstationary covariance models for multivariate processes defined on a sphere. On the other hand, the development of covariance models for geostatistical data should accompany methodologies for thorough goodness-of-fit diagnostics of the proposed models. The goal of this project is to provide in-depth development of multivariate spatial (-temporal) covariance models on a spherical domain that address certain nonstationary properties of the covariance structures, in small and large scale, paired with thorough goodness-of-fit diagnostics of the proposed models. Proposed covariance models are flexible to capture complex nonstationarity, such as varying smoothness and geometric anisotropy. The investigator develops Bayesian and non-Bayesian methods for goodness-of-fit diagnostics and studies the effect of plug-in estimators of covariance models. The investigator applies the models developed in this project to the problem of validating multiple climate model outputs from the CMIP5 archive with thorough diagnostics of the model fits. Different covariance structures over land and the ocean, as well as their dependence on latitude, are thoroughly investigated. The investigator also explores efficient computation methods for large data sets. The motivation of this project is the scientific problem of combining multiple climate model outputs and studying the relationships between different climate variables. A great deal of effort is being invested in developing state-of-the-art climate models by climate scientists worldwide, and a new set of climate model outputs (CMIP5-Coupled Model Intercomparison Project Phase 5), that are the basis of the results in the fifth assessment report of the Intergovernmental Panel on Climate Change (IPCC), are becoming available. This project will provide climate scientists and climate modelers with useful tools to intercompare and combine climate models and test the improvement of the CMIP5 results over the previous CMIP3 results. Statistical models developed in this project will enable more accurate assessments of the relationships between multiple climate variables such as temperature and precipitation, and future climate change.